Flat cables consist of a multiplicity of conductors embedded in a flat insulating plastic, the conductors most commonly being parallel to each other. Cable clamps are used to hold flat cables in an orderly arrangement in, for example a computer. Two or more cables often run in the same direction for some distance and, therefore, it is often desirable to mount a plurality of cables with a single cable clamp. The prior art includes U-shaped cable clamps with spring loaded legs to accommodate a plurality of flat cables but from which cables are too easily removed for many applications. A clamp more securely retaining the flat cables is disclosed in U.S. Pat. No. 3,971,105; but this clamp consists of three pieces, making it overly expensive and cumbersome to use. More recently, a one piece plastic cable clamp with a latching cover has been developed, as disclosed in U.S. Pat. No. 4,221,352. This cable clamp, however, suffers from the deficiency that when its capacity is fully used a new longitudinal run must be found for any further cables.